find n. (n!)²- 4n! - 12 = 0
Answers
Answer:
n=6 , n=-2
Step-by-step explanation:
[tex]n^{2}-4n-12=0[/tex]
Factorise to give:
[tex](n-6)(n+2)[/tex]
Set first one to equal 0:
[tex]n-6=0[/tex]
[tex]n=6[/tex]
Set second one to equal 0:
[tex]n+2=0[/tex]
[tex]n=-2[/tex]
Reason for 2 solutions:
All quadratics can have a maximum of 2 solutions like this one or a minimum of 0.
The solution(s) is the point where the graph crosses the x-axis
The image below shows the graph of the equation:
[tex]n^{2}-4n-12[/tex]
When y=0:
It intercepts the x-axis at 6 and -2 giving why n has 2 solutions
Related Questions
Which numbers on the spinner
have less than a 25% probability
of being spun?
Answers
Answer:
1
Step-by-step explanation:
I not completely sure but I think it 1
What percent of 38 is 12
Answers
[tex]Hiya![/tex]
Sokka is here to help!!
Here's a explanation!
[tex]\frac{38}{100} (12)[/tex]
[tex]=(\frac{38}{100} )(\frac{12}{1} )[/tex]
[tex]=(\frac{19}{50} )(\frac{12}{1} )[/tex]
[tex]=\frac{(19)(12)}{(50)(1)}[/tex]
[tex]=\frac{228}{50}[/tex]
[tex]=\frac{114}{25}[/tex]OR[tex]4.56[/tex]
ANSWER:
[tex]\frac{114}{25}, OR: 4.56[/tex]
Hopefully, this helps you!!
[tex]Sokka[/tex]
calculation of
24 – 16 ÷ 4 x 2 + 3
Answers
Answer:
19
Step-by-step explanation:
BODMAS
Brackets.
Of
Division
Multiplication
Addition and
Subtraction
go according to the BODMAS rule and solve the division first
24-(16÷4)×2+3
Then solve the multiplication part
24-(4×2)+3
Now solve like a regular sum
24-8+3
16+3
19
Three more than the product of 24 and Matt's height
Answers
Answer:
24m + 3 or (24 × m) + 3
Step-by-step explanation:
product = multiplying
matts height = variable
more than = addition
add together and that's your algebraic expression hope this helps :)
If y ∝ 1∕x and y = –2 when x = 14, find the equation that connects x and y.
A) y = –28x
B) y = –7x
C) y = –28∕x
D) y = –7∕x
Answers
Answer:
C
Step-by-step explanation:
Given y ∝ [tex]\frac{1}{x}[/tex] then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
To find k use the condition y = - 2 when x = 14 , then
- 2 = [tex]\frac{k}{14}[/tex] ( multiply both sides by 14 )
- 28 = k
y = - [tex]\frac{28}{x}[/tex] ← equation of variation
An object starts from rest with a constant acceleration of 2m/s^2 along a straight line. Find the distance travelled for the interval of 10 s.
Answers
Answer:
Distance is 100 m
Step-by-step explanation:
From second equation of motion;
[tex]{ \rm{s = ut + \frac{1}{2} {at}^{2} }} \\ [/tex]
s is displacementu is initial velocity, u = 0 [ from rest ]a is acceleration, a = 2 m/s²t is time, t = 10s[tex]{ \rm{s = (0 \times 10) + ( \frac{1}{2} \times 2 \times {10}^{2}) }} \\ \\ { \rm{s = {10}^{2} }} \\ \\ { \rm{s = 100 \: {m} }}[/tex]
The distance covered is 200m
Data;
acceleration = 2m/s^2time = 10sdistance = ?Distance CoveredTo find the distance covered by the object, we have to use the formula
of velocity. But we are not given the velocity or speed of the object here.
[tex]v = s/t[/tex]
where s and t are the distance and time respectively.
But from acceleration,
[tex]a = v/t\\v = a*t\\v = 2 * 10 \\v = 20m/s[/tex]
The velocity of the object is 20m/s
let's use this to find the distance covered.
[tex]v = s/t\\20 = s/10\\s = 20*10\\s= 200m\\[/tex]
The distance covered is 200m
Learn more on acceleration, distance, velocity and time here;
https://brainly.com/question/6078363
A rock is launched from a cannon. Its height, h(x), can be represented by a
quadratic function in terms of time, x, in
seconds.
After 1 second, the rock is 94 feet in the
air; after 2 seconds, it is 176 feet in the
air.
Complete the height function, h(x), for this situation
h(x) =
Answers
Answer:
The height, in feet, of the rock after 5 seconds = 875 feet
Step-by-step explanation:
i was doing this task in math and I came across this: x-12x=0.88x . can someone plz explain why is this equal to this? I understand it's simplified, but how?
Answers
1x-12x=0.88x
1x-12x=0.88x
11x=0.88x
-11x=0.88x-0.88x
-11.88x=0x
-11.88x=0
Isolate x
A salesperson will earn a commission equal to 1/12 of the total sales. What is the commission earned on sales totaling $43,000?
Answers
Answer: $3583.33
Step by Step Explanation:
43,000 * 1/12 = 43,000/12 = $3583.33
Help w exponential functions pls
Answers
Answer:
Step-by-step explanation:
"end behavior" means what the is graph doing if you keep going off the page.
The symbol "x approaches negative infinity" is going off the page to the left. Both graphs are going up, up, up as you look at the x's going off the page to the left. See image.The last point of the g(x) on the table, when it's on the graph, you can see that curve hit bottom and turned up. So g(x) is going up, up, up as you look at all the x's going to the right. However the original graph, the green graph f(x), well, it's kind of flat, but it IS going down, down, down as you go off the page to the right.
So the end behavior is the same as x approaches negative infinity and different as x approaches infinity.
A cook has 32 ounces of a 5% apple cider vinegar that she wants to dilute to a 3% apple cider vinegar . How much water does she need to add to obtain that concentration?
Answers
The cook needs to add 21.3 ounces of water to obtain the concentration
The cook has 32 ounces of 5% apple cider vinegar.
The total apple cider vinegar the cook has is:
[tex]Total = 32 \times 5\%[/tex]
[tex]Total = 1.6[/tex]
Let the quantity of water be x.
To dilute 3% apple cider vinegar, the cook would make use of the following equation
[tex]Total = 3\%\times (Apple\ Cider\ Vinegar + Water)[/tex]
So, we have:
[tex]Total = 3\%\times (32 + x)[/tex]
Substitute 1.6 for total
[tex]1.6= 3\%\times (32 + x)[/tex]
Divide both sides by 3%
[tex]53.3=32 + x[/tex]
Subtract 32 from both sides
[tex]53.3-32= x[/tex]
[tex]21.3= x[/tex]
Rewrite as:
[tex]x = 21.3[/tex]
Hence, the cook needs to add 21.3 ounces of water
Read more about concentration at:
https://brainly.com/question/25833493
pls help... I need to write some words to post this
Answers
Answer:
k=100, n=3, 1.5625, 10
Step-by-step explanation:
To find n and k, we can plug x and z in.
First we can try this for (1,100). We will get:
[tex]100=\frac{k}{1^{n} }[/tex]
Since 1 to any power is 1, we can assume that the denominator is 1 and therefore k=100.
Armed with k=100, we can plug numbers into the second equation.
[tex]12.5=\frac{100}{2^{n} }[/tex]
Moving [tex]{2^{n} }[/tex] to the left side, we get:
[tex]2^n=\frac{100}{12.5} }=8[/tex]
therefore we can solve and we see that n=3.
We can do the same for x=4, but since we have n, k, and x, we can plug these in to get z
[tex]z=\frac{100}{4^{3}} =1.5625[/tex]
We will do the same as previous but instead plug in x
[tex]\frac{1}{10}=\frac{100}{x^{3} }[/tex]
We isolate [tex]x^{3}[/tex] and get
[tex]x^{3} =1000[/tex]
Therefore x=10
Pls help plz thank you
Answers
Answer:
14, 31, 62
Step-by-step explanation:
11 + 3 = 14
14*2 = 28
28 + 3 = 31
31*2=62
Consider the functions f(x) = 12^x and g(x)= -2(12)^x. Which transformations must be applied to function F to produce the graph of function g?
SELECT ALL CORRECT ANSWERS
Vertical stretch
Vertical Shift
Vertical Compression
Reflection over the x-axis
Horizontal Shift
Answers
Answer:
Step-by-step explanation:
g(x) = -2f(x)
Vertical stretch by virtue of the factor 2
Reflection over the x-axis by virtue of the factor -1
The transformations which must be applied to function F to produce the graph of function g are vertical stretch and reflection over the x-axis.
To transform the function f(x)=12ˣ into the function g(x)=−2(12)ˣ
Since g(x) is multiplied by -2 compared to f(x), this represents a vertical compression.
The absolute value of the multiplier indicates the degree of compression/stretch.
The negative sign in front of 2(12)ˣ in g(x) reflects the graph over the x-axis. This means that the graph of g(x) is reflected below the x-axis compared to f(x).
Hence, vertical stretch and reflection over the x-axis are the transformations which must be applied to function F to produce the graph of function g.
To learn more on Graph transformation click here:
https://brainly.com/question/28025572
#SPJ3
WILL MARK BRAINIEST!! 50 POINTS.
Part A: Describe two types of transformations that can be used to transform f(x) to g(x).
Part B: Solve for k in each type of transformation.
Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x).
Answers
Answer:
Part A: The two types of types of transformation are
1) Rotation of 11.3° about (1, 2)
2) By algebraic transformation
Part B:
Rotation by 11.3° and T(2 - y)×1/2 + x, 0)
Part C: The transformation that can be used to transform f(x) to g(x) is T(2 - y)×1/2 + x, 0)
Step-by-step explanation:
The coordinates through which the linear function f(x) passes = (1. 3) and (3, 13)
The coordinates through which the linear function g(x) passes = (1, 3) and (1, 13)
The equation for f(x) in slope and intercept form. y = m·x + c is given as follows;
The slope, m = (13 - 3)/(3 - 1) = 5
The equation in point and slope form is y - 3 = 5×(x -1)
y = 5·x - 5 + 3 = 5·x - 3
y = 5·x - 3
The equation for g(x) in slope and intercept form. y = m·x + c is given as follows;
The slope, m = (13 - 3)/(1 - 1) = ∞
∴ The equation in point and slope form is x = 1
Therefore, the two equations meet at the point (1, 2)
The transformation that can be used to transform f(x) to g(x) is T(2 - y)×1/2 + x, 0)
2) Another transformation that can be used is to rotate f(x) by the vertex angle as follows
Vertex angle is 90° - tan⁻¹(m) = 90° - tan⁻¹(5) ≈ 11.3°
Rotation of f(x) by 11.3° about (1, 2) gives g(x)
Hope this helped!
Among 2165 passenger cars in a particular region, 235 had only rear license plates. Among 330 commercial trucks, 50 had only rear license plates. A reasonable hypothesis is that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. Use a 0.10 significance level. Identify the P-value. Let population 1 correspond to the passenger cars and population 2 correspond to the commercial trucks. Let a success be a vehicle that only has a rear license plate Group of answer choices
Answers
Using the z-distribution, it is found that the p-value is of 0.0192.
At the null hypothesis, it is tested if commercial trucks owners do not violate laws requiring front license plates at a higher rate than owners of passenger cars, that is, the subtraction is of at most 0, hence:
[tex]H_0: p_2 - p_1 \leq 0[/tex]
At the alternative hypothesis, it is tested if commercial truck owners violate the laws more, that is, the subtraction is positive, hence:
[tex]H_1: p_2 - p_1 > 0[/tex]
For each sample, the size, the proportion and the standard error are given by:
[tex]n_1 = 2165, p_1 = \frac{235}{2165} = 0.1085, s_1 = \sqrt{\frac{0.1085(0.8915)}{2165}} = 0.0067[/tex]
[tex]n_2 = 330, p_1 = \frac{50}{330} = 0.1515, s_1 = \sqrt{\frac{0.1515(0.8485)}{330}} = 0.0197[/tex]
For the distribution of differences, the mean and the standard error are given by:
[tex]\overline{p} = p_2 - p_1 = 0.1515 - 0.1085 = 0.043[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.0067^2 + 0.0197^2} = 0.0208[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{s}[/tex]
In which [tex]p = 0[/tex] is the value tested at the null hypothesis.
Hence:
[tex]z = \frac{\overline{p} - p}{s}[/tex]
[tex]z = \frac{0.043 - 0}{0.0208}[/tex]
[tex]z = 2.07[/tex]
The p-value is found using a z-distribution calculator, for a right-tailed test, as we are testing if the proportion is more than a value, with z = 2.07.
Using the calculator, the p-value is of 0.0192.A similar problem is given at https://brainly.com/question/15545277
Which expression is equivalent to 142 +35 - 2142
7z(2-5-39)
7zy(2-5-3)
21-5-39
7(2z-5-39)
HELP FAST
Answers
7 (2x +5 -3y)
help how do I do this!!!!
Answers
Answer:
C
Step-by-step explanation:
Since the weight is proportional to the cost, let's find the slope of the chart.
(x,y) corresponds to (weight, cost)
Pick 2 coordinate points with both the weight and cost.
(4, 23.96) (6, 35.94)
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{35.94-23.96}{6-4}= 5.99[/tex]
One pound is 5.99 dollars.
So to fill in the chart, multiply 5.99 by the number of pounds.
y=5.99x
2 lbs | $11.98
3 lbs | $17.97
4 lbs | $23.96
5 lbs | $29.95
6 lbs | $35.94
With this information, C would be the correct answer.
If you borrow $2,000 at 5 percent simple interest, how much will you owe
after one year?
O A. You will owe the principal of $2,000 only.
O B. You will owe the principal of $2,000 minus 5 percent of the
principal
O c. You will owe the principal of $2,000 plus 5 percent of the principal.
Answers
Answer:
it is c I think that it is c good luck
A television is advertised as having a 65-inch measurement. Brenan measures the width of the television while at the store and finds that it is 57 inches wide.
If the space where Brenan plans to hang the television is 32 inches high, will he have enough vertical space to hang the 65-inch television?
Answers
Answer: the answer would be C
Yes, the television is approximately 8 inches shorter than the space.
Step-by-step explanation: My name is Ebenezer Haile
The sum of two numbers is 20. The greater number is 4 more than three times the smaller number.
Answers
Answer:
And x=12 are the two numbers.
Step-by-step explanation:
x+y=20-----(1)
Let x be the larger number of the two.
x=2y-4
Hence 4=2y-x------(2)
Adding (1) and (2) we get 3y=24 so y=8
And x=12 are the two numbers.
Describe how to find your x-intercepts ?
Answers
Pleasee help with this question
Answers
Answer:
(2 x^2 z^13)/(z^8 y^5)
Hope This Helps!!!
Answer:
2xz⁵/y⁴
Step-by-step explanation:
16/8 = 2
x²/x = x
y/y⁵ = y⁻⁴
z¹³/z⁸ = z⁵
please help ill mark brainliest
Answers
Answer:
Pretty sure it is SAS as the angles are congruent
Step-by-step explanation:
Answer:
number 4
Step-by-step explanation:
both triangles use the aa as a point
If a recipe uses 5 cups of flour for every 2 cups of sugar, how much sugar is used for every 1 cup of flour?
Answers
2/5 cup of sugar
you divide 5 by 5 to get 1 cup of flour, and you divide 2 by 5 to get 2/5 cup of sugar
What is the result of 3/ 1/6
2
9
18
27
Answers
Step-by-step explanation:
remember 3 things
1. 3 = 3/1 (any integer is also a fraction of itself divided by 1).
2. 3 / 1/6 = 3/1 / 1/6 = 3/1 × 6/1 (dividing by a fraction is the same as multiplying with the upside-down fraction).
3 a/b × c/d = ac / bd. in our case 3/1 × 6/1 = 18/1 = 18
A line segment has endpoints at (3, 5) and (6, 1)
What is the x-coordinate of the midpoint?
Answers
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{1}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{6+3}{2}~~,~~\cfrac{1+5}{2} \right)\implies \left( \cfrac{9}{2}~~,~~\cfrac{6}{2} \right)\implies \left(4\frac{1}{2}~~,~~3 \right)[/tex]
Select Is a Function or is not a Function to correctly classily each relation
Is a Function
is not a Function
{(2, 2), (4,4), (6, 6), (8, 8)}
{(0,3), (3,5), (5, 6), (8, 4);
118
{(1, 2, (3, 3), (4, 8), (6,3)}
02
{(3, 4), (5,2), (5, 6), (7,3)}
Answers
Answer:
1: NOT A FUNCTIN
Step-by-step explanation:
MARKING AS BRAINLIEST!! Starr if given functions are inverse)!
Answers
========================================================
Explanation:
Start with the f(x) function. Then plug in g(x) like so
[tex]f(x) = 4x+3\\\\f(g(x)) = 4(g(x))+3\\\\f(g(x)) = 4\left(\frac{1}{4}x-\frac{3}{4}\right)+3\\\\f(g(x)) = 4\left(\frac{1}{4}x\right)+4\left(-\frac{3}{4}\right)+3\\\\f(g(x)) = x-3+3\\\\f(g(x)) = x\\\\[/tex]
----------------------------
Now we'll start with the g(x) function and then plug in f(x)
[tex]g(x) = \frac{1}{4}x-\frac{3}{4}\\\\g(f(x)) = \frac{1}{4}(f(x))-\frac{3}{4}\\\\g(f(x)) = \frac{1}{4}(4x+3)-\frac{3}{4}\\\\g(f(x)) = \frac{1}{4}(4x)+\frac{1}{4}(3)-\frac{3}{4}\\\\g(f(x)) = x+\frac{3}{4}-\frac{3}{4}\\\\g(f(x)) = x\\\\[/tex]
----------------------------
We've shown that the two equations are true
f(g(x)) = xg(f(x)) = xTherefore, f and g are inverses of each other.
HELP, pANYONE PLEASE !!!!
Answers
Answer:
A
Step-by-step explanation:
The line starts at -35, meaning that she starts the ascent 35 meters below the surface and goes upwards over time.
Answer:
a
Step-by-step explanation:
the starting point of the graph or also known as the y axis starts at -35
